This list is incomplete and I will be updating it as I create more circuits.
I will also accept circuits submitted in the comments if they are not already on the list or if they are more compact.

I have made a half adder so far and I will keep adding more that I find or make
Created by Gabu

---

Created by Gabu

This is about as compact as I can make it for now

---

Traces on the left are the carry and tile according to the image
Created by dbomblauncher2

---

5x5 Adder
Created by CallMeRetro [VR or Bust]

---

Nukebommer360 has made some interesting adders. This first one is quiet normal as the inputs are on the opposite side of the outputs. However the next one is a bit different.

6x4 Adder













This next one is also made by Nukebommer360 and it has a bit of a strange design as the inputs are on the side. This is a little odd but with its slim size I'm sure it will still work just fine in any circuit.

6x3 Adder with "wack inputs"

Here will be a compilation of ALUs
blueprint:

This is a very simple ALU design I have made that has six instructions from the top down:
Carry
Add
Not
Xor
Or
And

Created by Gabu

---

Created by Gabu

A newer and bigger ALU I have made including 4 new instructions!
Colors represent the following:
Green, A input
Red, B input
Purple, Control Lines
Blue, Output lines
White, inner connections

The control lines are in charge of choosing which output is produced. The instructions are as follows from top to bottom:
Carry
Add
Greater than, (Will output 1 if A is greater than b)
Equal to, (Will output 1 if A and B are equal)
Shift Right
Shift Left
Not
Xor
Or
And

---

---

Here is a small parallel register cell I came up with
blueprint:
Created by Gabu

The write is on the right and the input is on the left

---

Left Input is Write. Right Input is Data.
Created by dbomblauncher2

RAM

I came up with this memory cell, I couldn't get it any smaller
blueprint:

Created by Gabu

From left to right: Select, Input, Read/Write

---

Created by Parzival Wolfram

Parzival modified one of Ortega's gate designs to make a 4-bit memory setup. He says it's not the most compact design, but it works pretty well

Yellow traces are data, dark blue are cell selection, red is load enable, light blue is save enable. To change cell number, exchange the appropriate NOT gates in the dark-blue section with buffers.

Note from Gabu: Output and input are on the same trace. It would also seem that this design has the binary-decimal decoders located at each cell instead of being grouped together. Just thought that was interesting.

---

Note: This blueprint is for the beta release and will not work if you are not on the beta

6x7 Memory Cell created by Metalboy

Blue is read, Yellow is write, and green is input/output














A tiled example of this cell:

---

Created by AlexChecker


This is a very interesting design that utilizes busses and multicolored traces to more easily compact ram. This way, the memory can cells can take up less horizontal space if that is what your design calls for. Though immediately i can only be used for 8 bit designs, this could be easily modified to fit any multiple of 8.

The green bus carries the read and write signal which are white and gray respectively
The red bus carries the output signal which contains trace colors red through turquoise
The blue bus carries the input signal which also contains trace colors red through turquoise

---

Created by Gabu

uses latches to signify an on or off signal

Vertical Wire is the activation, Horizontal Wire is the output.

---

Created by Erikbot

Write heads signify an on signal and traces signify an off signal

I'm not quite sure what I should call this section but I hope it fits what I put in here.

---

Created by Gabu

This monster is the first iteration of my greater than circuit. The top and bottom (green traces are inputs) have the most significant bit located on the left side. The blue is the output signal. On means that the A input is greater than the B input. Off means that the numbers are equal or A is less than B.
The blueprint is just a single cell but it tiles according to the image.

I'm going put circuits here that don't fit into any big category.

---

Created by Gabu
Using dbomblauncher2's register

The left inputs are data and the right inputs are write.
There is a button on the left you can click to activate the clock

---

I've had a lot of trouble on my CPUS with my clock cascading backwards and activating other lines of code accidentally. I made this design so that each cycle only one signal is sent.

---

Created by robotosaurus

This is a very dense multiplexer and It seems very easily stackable to be able to create multi-bit multiplexers.
Note that this only will be able to switch between two inputs in its current state.